{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true,
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "# Learn to Throw\n",
    "[![Google Collab Book](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/tum-pbs/PhiFlow/blob/develop/docs/Learn_to_Throw_Tutorial.ipynb)\n",
    "\n",
    "In this notebook, we will train a fully-connected neural network to solve an inverse ballistics problem.\n",
    "We will compare supervised training to differentiable physics training, both numerically and visually.\n",
    "\n",
    "[**Φ-Flow**](https://github.com/tum-pbs/PhiFlow)\n",
    "&nbsp;&nbsp;&nbsp; [**Documentation**](https://tum-pbs.github.io/PhiFlow/)\n",
    "&nbsp;&nbsp;&nbsp; [**API**](https://tum-pbs.github.io/PhiFlow/phi)\n",
    "&nbsp;&nbsp;&nbsp; [**Demos**](https://github.com/tum-pbs/PhiFlow/tree/master/demos)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [],
   "source": [
    "# !pip install phiflow"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [],
   "source": [
    "# from phi.tf.flow import *\n",
    "from phi.torch.flow import *\n",
    "# from phi.jax.stax.flow import *"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "To define the physics problem, we write a function to simulate the forward physics. This function takes the initial position, height, speed and angle of a thrown object and computes where the object will land, assuming the object follows a parabolic trajectory. Neglecting friction, can compute this by solving a quadratic equation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": "\u001B[94m11.414213\u001B[0m"
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def simulate_hit(pos, height, vel, angle, gravity=1.):\n",
    "    vel_x, vel_y = math.cos(angle) * vel, math.sin(angle) * vel\n",
    "    height = math.maximum(height, .5)\n",
    "    hit_time = (vel_y + math.sqrt(vel_y**2 + 2 * gravity * height)) / gravity\n",
    "    return pos + vel_x * hit_time, hit_time, height, vel_x, vel_y\n",
    "\n",
    "simulate_hit(10, 1, 1, 0)[0]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "Let's plot the trajectory! We define *y(x)* and sample it on a grid. We have to drop invalid values, such as negative flight times and below-ground points."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": "<Figure size 864x360 with 1 Axes>"
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": "<Figure size 864x360 with 1 Axes>",
      "image/png": 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\n"
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "def sample_trajectory(pos, height, vel, angle, gravity=1.):\n",
    "    hit, hit_time, height, vel_x, vel_y = simulate_hit(pos, height, vel, angle, gravity)\n",
    "    def y(x):\n",
    "        t = (x.vector[0] - pos) / vel_x\n",
    "        y_ = height + vel_y * t - gravity / 2 * t ** 2\n",
    "        return math.where((y_ > 0) & (t > 0), y_, NAN)\n",
    "    return CenteredGrid(y, x=2000, bounds=Box(x=(min(pos.min, hit.min), max(pos.max, hit.max))))\n",
    "\n",
    "vis.plot(sample_trajectory(tensor(10), 1, 1, math.linspace(-PI/4, 1.5, channel(linspace=7))), title=\"Varying Angle\")"
   ]
  },
  {
   "cell_type": "markdown",
   "source": [
    "Before we train neural networks on this problem, let's perform a classical optimization using gradient descent in the initial velocity `vel`. We need to define a loss function to optimize. Here we desire the object to hit at `x=0`."
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%% md\n"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "outputs": [
    {
     "data": {
      "text/plain": "\u001B[94m50.0\u001B[0m"
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "vel = tensor(1)\n",
    "\n",
    "def loss_function(vel):\n",
    "  return math.l2_loss(simulate_hit(10, 1, vel, 0)[0] - 0)\n",
    "\n",
    "loss_function(0)"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n"
    }
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "Φ<sub>Flow</sub> uses the selected library (PyTorch/TensorFlow/Jax) to derive analytic derivatives.\n",
    "By default, the gradient function also returns the function value."
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%% md\n"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "outputs": [
    {
     "data": {
      "text/plain": "(\u001B[94m65.14213\u001B[0m, [\u001B[94m16.142136\u001B[0m])"
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gradient = math.functional_gradient(loss_function, get_output=True)\n",
    "gradient(vel)"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "vel=\u001B[94m-2.2284272\u001B[0m - loss=\u001B[94m65.14213\u001B[0m\n",
      "vel=\u001B[94m-4.1654835\u001B[0m - loss=\u001B[94m23.451168\u001B[0m\n",
      "vel=\u001B[94m-5.3277173\u001B[0m - loss=\u001B[94m8.442421\u001B[0m\n",
      "vel=\u001B[94m-6.0250573\u001B[0m - loss=\u001B[94m3.0392709\u001B[0m\n",
      "vel=\u001B[94m-6.4434614\u001B[0m - loss=\u001B[94m1.0941381\u001B[0m\n",
      "vel=\u001B[94m-6.694504\u001B[0m - loss=\u001B[94m0.39388976\u001B[0m\n",
      "vel=\u001B[94m-6.8451295\u001B[0m - loss=\u001B[94m0.14180061\u001B[0m\n",
      "vel=\u001B[94m-6.935505\u001B[0m - loss=\u001B[94m0.051048037\u001B[0m\n",
      "vel=\u001B[94m-6.9897304\u001B[0m - loss=\u001B[94m0.018377367\u001B[0m\n",
      "vel=\u001B[94m-7.0222654\u001B[0m - loss=\u001B[94m0.0066157645\u001B[0m\n"
     ]
    },
    {
     "data": {
      "text/plain": "<Figure size 864x360 with 1 Axes>"
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": "<Figure size 864x360 with 1 Axes>",
      "image/png": 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\n"
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "trj = [vel]\n",
    "for i in range(10):\n",
    "  loss, (grad,) = gradient(vel)\n",
    "  vel = vel - .2 * grad\n",
    "  trj.append(vel)\n",
    "  print(f\"vel={vel} - loss={loss}\")\n",
    "trj = math.stack(trj, channel('opt'))\n",
    "vis.plot(sample_trajectory(tensor(10), 1, trj, 0))"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n"
    }
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "Now we can just subtract the gradient times a learning rate $\\eta = 0.2$ until we converge."
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%% md\n"
    }
   }
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "Next, we generate a training set and test by sampling random values."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [],
   "source": [
    "def generate_data(shape):\n",
    "  pos = math.random_normal(shape)\n",
    "  height = math.random_uniform(shape) + .5\n",
    "  vel = math.random_uniform(shape)\n",
    "  angle = math.random_uniform(shape) * PI/2\n",
    "  return math.stack(dict(pos=pos, height=height, vel=vel, angle=angle), channel('vector'))\n",
    "\n",
    "x_train = generate_data(batch(examples=1000))\n",
    "x_test = generate_data(batch(examples=1000))\n",
    "y_train = simulate_hit(*x_train.vector)[0]\n",
    "y_test = simulate_hit(*x_test.vector)[0]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "Now, let's create a fully-connected neural network with three hidden layers. We can reset the `seed` to make the weight initialization predictable."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "DenseNet(\n",
       "  (linear0): Linear(in_features=1, out_features=32, bias=True)\n",
       "  (linear1): Linear(in_features=32, out_features=64, bias=True)\n",
       "  (linear2): Linear(in_features=64, out_features=32, bias=True)\n",
       "  (linear3): Linear(in_features=32, out_features=4, bias=True)\n",
       ")"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "math.seed(0)\n",
    "net_sup = dense_net(1, 4, [32, 64, 32])\n",
    "net_sup"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([-0.0075,  0.5884, -0.7979, -0.7646, -0.4088,  0.3018,  0.0102,  0.8287,\n",
       "        -0.1134,  0.3327, -0.3164, -0.1966, -1.0038, -0.7402, -0.3952,  0.0130,\n",
       "         0.4065,  0.6272, -0.6946, -0.4294,  0.3627,  0.7943, -0.1923,  0.7780,\n",
       "        -0.0978,  0.1058,  0.9469, -0.9768, -0.5935, -0.1818, -0.4428,  0.8677],\n",
       "       device='cuda:0')"
      ]
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# net_sup.trainable_weights[0]  # TensorFlow\n",
    "net_sup.state_dict()['linear0.weight'].flatten()  # PyTorch\n",
    "# net_sup.parameters[0][0]  # Stax"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "For the differentiable physics network we do the same thing again."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([-0.0075,  0.5364, -0.8230, -0.7359, -0.3852,  0.2682, -0.0198,  0.7929,\n",
       "        -0.0887,  0.2646, -0.3022, -0.1966, -0.9553, -0.6623, -0.4122,  0.0370,\n",
       "         0.3953,  0.6000, -0.6779, -0.4355,  0.3632,  0.8304, -0.2058,  0.7483,\n",
       "        -0.1612,  0.1058,  0.9055, -0.9277, -0.6295, -0.2532, -0.3898,  0.8640],\n",
       "       device='cuda:0')"
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "math.seed(0)\n",
    "net_dp = dense_net(1, 4, [32, 64, 32])\n",
    "# net_dp.trainable_weights[0]  # TensorFlow\n",
    "net_dp.state_dict()['linear0.weight'].flatten()  # PyTorch\n",
    "# net_dp.parameters[0][0]  # Stax"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "Indeed, the We see that the networks were initialized identically! Alternatively, we could have saved and loaded the state."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "## Supervised Training\n",
    "Now we can train the network. We feed the desired hit position into the network and predict a possible initial state.\n",
    "For supervised training, we compare the network prediction to the ground truth from our training set."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Supervised loss (training set): \u001B[92m(examplesᵇ=1000)\u001B[0m \u001B[93mfloat32\u001B[0m  \u001B[94m0.270 ± 0.179\u001B[0m \u001B[37m(3e-03...1e+00)\u001B[0m\n",
      "Supervised loss (test set): \u001B[92m(examplesᵇ=1000)\u001B[0m \u001B[93mfloat32\u001B[0m  \u001B[94m0.285 ± 0.187\u001B[0m \u001B[37m(1e-02...1e+00)\u001B[0m\n"
     ]
    }
   ],
   "source": [
    "opt_sup = adam(net_sup)\n",
    "\n",
    "def supervised_loss(x, y, net=net_sup):\n",
    "  prediction = math.native_call(net, y)\n",
    "  return math.l2_loss(prediction - x)\n",
    "\n",
    "print(f\"Supervised loss (training set): {supervised_loss(x_train, y_train)}\")\n",
    "print(f\"Supervised loss (test set): {supervised_loss(x_test, y_test)}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Supervised loss (training set): \u001B[92m(examplesᵇ=1000)\u001B[0m \u001B[93mfloat32\u001B[0m  \u001B[94m0.266 ± 0.176\u001B[0m \u001B[37m(3e-03...1e+00)\u001B[0m\n",
      "Supervised loss (test set): \u001B[92m(examplesᵇ=1000)\u001B[0m \u001B[93mfloat32\u001B[0m  \u001B[94m0.282 ± 0.184\u001B[0m \u001B[37m(1e-02...1e+00)\u001B[0m\n"
     ]
    }
   ],
   "source": [
    "for i in range(100):\n",
    "  update_weights(net_sup, opt_sup, supervised_loss, x_train, y_train)\n",
    "\n",
    "print(f\"Supervised loss (training set): {supervised_loss(x_train, y_train)}\")\n",
    "print(f\"Supervised loss (test set): {supervised_loss(x_test, y_test)}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "What? That's almost no progress! Feel free to run more iterations but there is a deeper problem at work here. Before we get into that, let's train a the network again but with a differentiable physics loss function."
   ]
  },
  {
   "cell_type": "markdown",
   "source": [
    "## Training with Differentiable Physics\n",
    "For the differentiable physics loss, we simulate the trajectory given the initial conditions predicted by the network. Then we can measure how close to the desired location the network got."
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%% md\n"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Supervised loss (training set): \u001B[92m(examplesᵇ=1000)\u001B[0m \u001B[93mfloat32\u001B[0m  \u001B[94m1.709 ± 0.823\u001B[0m \u001B[37m(3e-01...6e+00)\u001B[0m\n",
      "Supervised loss (test set): \u001B[92m(examplesᵇ=1000)\u001B[0m \u001B[93mfloat32\u001B[0m  \u001B[94m1.753 ± 0.855\u001B[0m \u001B[37m(4e-01...6e+00)\u001B[0m\n"
     ]
    }
   ],
   "source": [
    "def physics_loss(y, net=net_dp):\n",
    "  prediction = math.native_call(net, y)\n",
    "  y_sim = simulate_hit(*prediction.vector)[0]\n",
    "  return math.l2_loss(y_sim - y)\n",
    "\n",
    "opt_dp = adam(net_dp)\n",
    "\n",
    "for i in range(100):\n",
    "  update_weights(net_dp, opt_dp, physics_loss, y_train)\n",
    "\n",
    "print(f\"Supervised loss (training set): {supervised_loss(x_train, y_train, net=net_dp)}\")\n",
    "print(f\"Supervised loss (test set): {supervised_loss(x_test, y_test, net=net_dp)}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "This looks even worse! The differentiable physics network seems to stray even further from the ground truth.\n",
    "Well, we're not trying to match the ground truth, though. Let's instead measure how close to the desired location the network threw the object."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {
    "scrolled": true,
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Supervised network (test set): \u001B[92m(examplesᵇ=1000)\u001B[0m \u001B[93mfloat32\u001B[0m  \u001B[94m0.003 ± 0.001\u001B[0m \u001B[37m(5e-04...2e-02)\u001B[0m\n",
      "Diff.Phys. network (test set): \u001B[92m(examplesᵇ=1000)\u001B[0m \u001B[93mfloat32\u001B[0m  \u001B[94m1.90e-04 ± 1.5e-03\u001B[0m \u001B[37m(9e-11...4e-02)\u001B[0m\n"
     ]
    }
   ],
   "source": [
    "print(f\"Supervised network (test set): {physics_loss(y_test, net=net_sup)}\")\n",
    "print(f\"Diff.Phys. network (test set): {physics_loss(y_test, net=net_dp)}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "Now this is much more promissing. The diff.phys. network seems to hit the desired location very accurately considering it was only trained for 100 iterations. With more training steps, this loss will go down even further, unlike the supervised network.\n",
    "\n",
    "So what is going on here? Why does the supervised network perform so poorly?\n",
    "The answer lies in the problem itself. The task is multi-modal, i.e. there are many initial states that will hit the same target.\n",
    "The network only gets the target position and must decide on a single initial state. With supervised training, there is no way to know which ground truth solution occurs in the test set. The best the network can do is average nearby solutions from the training set. But since the problem is non-linear, this will give only a rough guess.\n",
    "\n",
    "The diff.phys. network completely ignores the ground truth solutions which are not even passed to the `physics_loss` function. Instead, it learns to hit the desired spot, which is exactly what we want.\n",
    "\n",
    "We can visualize the difference by looking at a couple of trajectories."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "scrolled": false,
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\PhD\\phiflow2.1\\phi\\math\\_shape.py:1294: RuntimeWarning: Stacking shapes with incompatible item names will result in item names being lost. Got ('pos', 'height', 'vel', 'angle') and None\n",
      "  warnings.warn(f\"Stacking shapes with incompatible item names will result in item names being lost. Got {item_names[index]} and {items}\", RuntimeWarning)\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1152x288 with 4 Axes>"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 432x288 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "predictions = math.stack({\n",
    "    \"Ground Truth\": x_test.examples[:4],\n",
    "    \"Supervised\": math.native_call(net_sup, y_test.examples[:4]),\n",
    "    \"Diff.Phys\": math.native_call(net_dp, y_test.examples[:4]),\n",
    "}, channel('curves'))\n",
    "vis.plot(sample_trajectory(*predictions.vector), size=(16, 4))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "We can see that the differentiable physics network matches the hit point much more precisely than the supervised network, as expected from the loss values."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}